Clusters in a group: decision making in the vector space formulation of the analytic hierarchy process

Article Abstract:

A study was conducted to characterize the use of an algorithm to organize individuals into natural clusters based on a similarity measure. The coherence of the cluster was also analyzed. A heuristic algorithm was implemented in C++ and was utilized to evaluate the algorithm. Results indicated that the clustering algorithm can be utilized in various disciplines such as corporate restructuring, group technology and astronomy, and can be enhanced by analyzing the final cluster structures.

Operations Research, Analysis, Usage, Algorithms, Decision-making, Group, Group decision making, Heuristic programming

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Geometry of decision making and the vector space formulation of the analytic hierarchy process

Article Abstract:

Research was conducted to examine the Euclidean vector space reformulation of the Analytic Hierarchy Process (AHP) methodologies. The objective was to demonstrate that the formulation conforms to the results of the conventional AHP. An aggregation scheme for the calculation of the group preference from individual preferences using a simple vector addition procedure that satisfies Pareto optimality condition is proposed. Results are in good agreement with conventional AHP results.

Decision-making, Decision making, Vector spaces, Vectors (Mathematics), Scalar field theory, Linear topological spaces

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Consequences of uncertainty in the analytic hierarchy process: a simulation approach

Article Abstract:

The propagation of uncertainty in the decision process modelling tool known as Analytic Hierarchy Process (AHP) is considered. Specifically, a simulation approach is taken to determine the probability of rank reversal over a range of judgmental uncertainties arising from doubts articulated by a decision maker concerning the accuracy of his or her observations. In addition, an aggregate measure of uncertainty in the eigenvector of the preference matrices is proposed.

Operations research, Management science, Case studies, Simulation methods, Simulation, Uncertainty, Statistical decision, Statistical decision theory

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